Such turbine blades are generally known. They have an airfoil section which is subjected to flow of a hot working medium and extends from a leading edge to a trailing edge. The airfoil section in this case is formed by a blade wall on the suction side and a blade wall on the pressure side and is provided with a coating on its outer surface which faces the hot working medium. The coating serves as a thermal barrier coating in order to minimize the heat yield from the hot working medium to the material of the airfoil section, so that this can withstand the mechanical and thermal stresses for a predetermined service life. Although this coating, for example a ceramic APS thermal barrier coating, protects the turbine blade material, cracks can occur in the blade material as wear phenomena, which shorten the service life of the component and which can endanger the operation of the gas turbine with the absence of countermeasures.